Ju l 1 99 9 GEOMETRICAL DESCRIPTION OF VORTICES IN GINZBURG - LANDAU BILLIARDS
نویسندگان
چکیده
2.5 *The Laplacian 2.6 Bibliography 3. Fiber bundles and their topology 3.1 Introduction 3.2 Local symmetries. Connexion and curvature 3.3 Chern classes 3.4 Manifolds with a boundary: Chern-Simons classes 3.4.1 The Gauss-Bonnet theorem 3.4.2 Surfaces with boundary 3.4.3 Secondary characteristic classes 3.5 *The Weitzenböck formula 4. The dual point of Ginzburg-Landau equations for an infinite system 4.1 The Ginzburg-Landau equations 4.2 The Bogomol'nyi identities 5. The superconducting billiard 5.1 The zero current line 5.2 A selection mechanism and topological phase transitions 5.3 A geometrical expression of the Gibbs potential for finite systems 2
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We study the linearized stability of n-vortex (n ∈ Z) solutions of the magnetic Ginzburg-Landau (or Abelian Higgs) equations. We prove that the fundamental vortices (n = ±1) are stable for all values of the coupling constant, λ, and we prove that the higher-degree vortices (|n| ≥ 2) are stable for λ < 1, and unstable for λ > 1. This resolves a long-standing conjecture (see, eg, [JT]).
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